Question

x² + 4x + 5 factries



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Answer 1

➺ Factorize : x² + 4x + 5

➺ x² - 4x - 5=0

x²-5x+x-5=0

x(x-5)+1(x-5)

(x-5)(x+1)=0

➺ x = 5 or x = -1

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Answer 2

Ohkay,

here we need to factorise the given expression....

First, let p(x) = x² + 4x + 5 = 0

Now here we are in need to check whether p(x) have any zero

to check we need to find D (discriminant) of the equation

where a = 1

b = 4

c = 5

Now putting these values in b² - 4ac we get

D = b² - 4ac

= (4)² - 4(1)(5)

= 16 - 20

= - 4

Here we came to observe that D < 0

There we must conclude that this equation don't have any real root and thus it's factorisation is impossible....

Key pointz to remember here...

• Since a quadratic polynomial is one which has a degree of 2.

e.g - p(x) = a + 7x + 7x²

Here in Polynomial of x we can see that maximum power which is being held by x is 2

• If we put a 0 (zero) in equal to the polynomial then the equation becomes a Quadratic Equation

e.g - x² + 6x - 89 = 0

• Every quadratic equation is in the following form

ax² + bx + c = 0

Where a ≠ 0

• To find the nature of roots of a certain quadratic equation we need to check what is the value of equation's discriminant (D).

Where D = b² - 4ac

There are three conditions on the basis of above equation

1. if D > 0 then .The roots of the given equation would be real but different. These equations can be factorise easily by Middle term splitting and Completing square method.
2. if D = 0 then the given equation will have two real but same roots. Such equations can be solved using suitable identities, specialy those that are based upon squaring.
3. If D < 0 then the given equation ( as we came to observe above) will not have any roots and thus it can't be factorised..

Hope, it will surely help You

Happy Learning....